68: INTERACTION SCREENING AND PSEUDOLIKELIHOOD APPROACHES FOR TENSOR LEARNING IN ISING MODELS

Music City Center 

The Ising model is a widely used discrete exponential family for modeling dependent binary data, originally developed in statistical physics to study ferromagnetism through pairwise interactions. However, many modern applications in fields like social science and biology require modeling higher-order, multi-body interactions. To address this, we study the p-tensor Ising model, which generalizes the classical Ising model by incorporating multi-linear sufficient statistics of degree p ⩾ 3 to capture complex dependencies. In this work, we develop structure learning methods to infer the underlying hypernetwork from observed data. We establish theoretical guarantees for two regularized estimators - pseudo-likelihood-based node-wise LASSO and interaction screening. We show that both these approaches, with proper regularization, retrieve the underlying hypernetwork structure using a sample size logarithmic in the number of network nodes, and exponential in the maximum interaction strength and maximum nodedegree. We also track down the exact dependence of the rate of tensor recovery on the interaction order p, which is allowed to grow with the number of samples and nodes, for both the approaches. We then provide a comparative discussion of the performance of the two approaches based on simulation studies, which also demonstrates the exponential dependence of the tensor recovery rate on the maximum coupling strength. Our tensor recovery methods are then applied on gene data taken from the Curated Microarray Database (CuMiDa), where we focused on understanding the important genes related to hepatocellular carcinoma.